It may be a sticky IAC. When you try a restart just give a little pedal (maybe 1/8 pedal), too much pedal and you may flood it. If the B+ latch relay is bad, it can also do this. A very marginal battery can also cause IAC issues.
A stuck open EGR valve can do the same thing, less likely but it can happen.
Most of the trouble with the IAC first becomes noticeable when you release the gas pedal, if it is in fact stuck shut, it starves the engine of air. Take a look at your air filter and see if it isn't very oil soaked, some oil doesn't often mean much, a lot can cause grief.
Often a bad CPS and you won't get any start or sometimes when the engine heats up it will stall and may run really bad or not at all. CPS can be unpredictable.